Figurative:
* A nose to the ground, following the scent.
* Driven by primal instinct, relentless in its pursuit.
* A feathered arrow, aimed at the heart of the chase.
* With a heart full of fire and a nose full of purpose.
* The embodiment of unyielding dedication.
Descriptive:
* A hound dog with a keen sense of smell, tracking its prey with unwavering focus.
* A tireless hunter, running with boundless energy.
* A skilled tracker, navigating the terrain with ease.
* A fierce predator, driven by the instinct to hunt.
* A loyal companion, always ready to follow its master's lead.
You can also choose to focus on a specific aspect of the hound dog's hunting behavior:
* A bloodhound, with its legendary sense of smell.
* A beagle, with its playful energy and tenacious spirit.
* A foxhound, known for its speed and endurance.
The best option will depend on the context of your writing.